Chapter 11: Q. 49 (page 794)

In Problems 49 and 50, graph each system of inequalities by hand.
$\{\begin{cases} x^{2} + y^{2} \leq 16 \\ x + y \geq 2 \end{cases}$

Short Answer

Expert verified

The graph of $\{\begin{cases} x^{2} + y^{2} \leq 16 \\ x + y \geq 2 \end{cases}$ is

Step by step solution

Step 1. Given data

The given system of inequality is

$\{\begin{cases} x^{2} + y^{2} \leq 16 \\ x + y \geq 2 \end{cases}$

Step 2. Properties of the graph of the inequality

Graph of $x^{2} + y^{2} = 16$ will be a circle of center $(0, 0)$

now test the origin point $(0, 0)$ for inequality $x^{2} + y^{2} \leq 16$

$x^{2} + y^{2} \leq 16 0^{2} + 0^{2} \leq 16 0 < 16$

inequality satisfied so the origin will lie in the region of inequality

So the region inside the circle will be shaded

Step 3. Properties of the graph of the inequality

Graph of $x + y = 2$ will be a line

now test the origin point $(0, 0)$ for inequality $x + y \geq 2$

$x + y \geq 2 0 + 0 \geq 2 0 < 2$

inequality does not satisfy so the origin will not lie in the region of inequality

So the region above from the line will be shaded

Step 4. graph of the system of inequality

The graph of the system of inequality is

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In Problems 49 and 50, graph each system of inequalities by hand.
$\{\begin{cases} x^{2} + y^{2} \leq 16 \\ x + y \geq 2 \end{cases}$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Properties of the graph of the inequality

Step 3. Properties of the graph of the inequality

Step 4. graph of the system of inequality

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In Problems 49 and 50, graph each system of inequalities by hand.x2+y2≤16x+y≥2

Short Answer

Step by step solution

Step 1. Given data

Step 2. Properties of the graph of the inequality

Step 3. Properties of the graph of the inequality

Step 4. graph of the system of inequality

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Pure Maths

Probability and Statistics

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 49 and 50, graph each system of inequalities by hand.
$\{\begin{cases} x^{2} + y^{2} \leq 16 \\ x + y \geq 2 \end{cases}$